1. Field of the Invention
The present disclosure relates generally to serial channel coding, and more particularly to techniques for transmitting and receiving a data sequence across an electrical serial channel.
2. Description of Related Art
For purposes of this disclosure, a serial channel in an electronic system comprises a signal path between a transmitter that transmits a single data stream containing all information necessary to receive the data stream and a receiver that receives the data stream. A typical serial channel transmitter transmits a series of equally-spaced symbols at a given symbol rate R. The receiver recovers the symbol rate and symbol timing from the received data, and uses the recovered timing to detect, for each symbol period, which symbol was transmitted.
A serial channel code determines the symbol sequence that will be transferred across a channel to represent a given data sequence. Serial channel codes require at least two symbols, although some codes use many more symbols. One typical method of transmission assigns a pulse of a given voltage level to each symbol. For high-speed transmission, the channel does not return to a quiescent level between successive symbols—this is known as Non-Return-to-Zero (NRZ) signaling.
FIG. 1A illustrates, for an exemplary binary input data stream S(i), binary channel coding using Pulse Amplitude Modulation (PAM). When S(i)=0, a first symbol amplitude S1 that represents “0” is transmitted, and when S(i)=1, a second symbol amplitude S2 that represents “1” is transmitted. Each symbol has a period T, where T=1/R. When either S1 or S2 is transmitted by sending no signal, this is known as “on-off” signaling. When S1=−S2, this is known as polar signaling. Other symbol choices can result in an offset polar signal that has a DC bias VB, i.e., where S1=2×VB−S2. Any of these signal types can also be transmitted differentially using two conductors, where a 0 is transmitted by sending S1 on the first conductor and sending S2 on the second conductor at the same time, and a 1 is transmitted by sending S2 on the first conductor and sending S1 on the second conductor at the same time.
Pulse Amplitude Modulation can use more than two symbol amplitudes. FIG. 1B shows an example for S(i) and PAM4 (four-level PAM) coding, and FIG. 1C shows an example for S(i) and PAM8 (eight-level PAM) coding. Turning first to PAM4 and FIG. 1B, with four signal levels available, each symbol can transmit two bits of information. One of the four signal levels is assigned to each of the possible two-bit patterns “00,” “01,” “10,” and “11.” S(i) is then transmitted two bits at a time, with each symbol having a period 2 T, e.g., 2/R.
With the FIG. 1C eight-level coding, each PAM8 symbol can transmit three bits of information. One of the eight signal levels is assigned to each of the possible three-bit patterns shown in FIG. 1C. S(i) is then transmitted three bits at a time, with each symbol having a period 3 T, e.g., 3/R. PAM4 and PAM8 can both be transmitted as polar signals or offset polar symbols.
The bandwidth required to transmit a PAM signal is proportional to the symbol rate. For instance, FIG. 2 shows a measured power spectral density (distribution of the transmitted signal power as a function of frequency) for NRZ polar signaling with a symbol rate R=2 Gbps (billion bits/second). The bulk of the transmitted power is concentrated in a main lobe between 0 Hz and 2 GHz. Additional sidelobes exist, with the first sidelobe peaking at about −12 dB around 3 GHz, the second sidelobe peaking at about −14 dB around 5 GHz, etc. (the waveform in this example was sampled at 10 GHz, and thus frequencies beyond 5 GHz are not shown).
The essential bandwidth necessary to transmit the FIG. 2 signal is approximately equal to the main lobe width, e.g., 2 GHz. In other words, should the channel attenuate the higher frequencies more than the main lobe frequencies, it should be possible to reliably receive the signal when noise power is controlled.
The primary advantage of PAM4 and PAM8 is a lower symbol rate, resulting in a proportionally narrower main lobe width, e.g., 1 GHz for PAM4 and 0.67 GHz for PAM8. Thus a channel that may be marginal for NRZ polar at 2 Gbps could perform well for 2 Gbps PAM4, with a 1 Gbps symbol rate, and even better for 2 Gbps PAM8, with a 0.67 Gbps symbol rate. One tradeoff, however, is that when the same symbol spacing used for NRZ is maintained, PAM4 and PAM8 require much more power. Another tradeoff is that the number of signaling levels (and thus transmitter and receiver complexity) increase as 2N, wherein N is the number of bits transmitted per symbol. Thus one quickly reaches a point of diminishing returns—the 25% bandwidth decrease available from going from PAM8 (3 bits/symbol) to PAM16 (4 bits/symbol), for example, requires 16 signal levels instead of 8.